双临界指数的薛定谔-泊松-斯莱特方程的基态解

doi:10.3969/j.issn.1006-8074.2026.01.005

数学理论与应用 ›› 2026, Vol. 46 ›› Issue (1): 72-.doi: 10.3969/j.issn.1006-8074.2026.01.005

双临界指数的薛定谔-泊松-斯莱特方程的基态解

邵玉米;雷春雨^*

贵州民族大学数据科学与信息工程学院, 贵阳 550025

出版日期:2026-03-28 发布日期:2026-04-23

Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents

Shao Yumi; Lei Chunyu^*

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Online:2026-03-28 Published:2026-04-23
Contact: Lei Chunyu; E-mail: leichygzu@sina.cn
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 12461024), the Science and Technology Foundation of

Guizhou Province (No. ZK[2024]059), and the Natural Science Research Project of Department of Education of Guizhou Province (No. QJJ2023062)

摘要/Abstract

摘要： 本文研究$\mathbb R^3$中含库仑-索伯列夫临界指数与索伯列夫临界指数的薛定谔-泊松-斯莱特方程. 这两个临界指数（分别为3和6）导致相关函数空间的嵌入映射不具紧性. 通过利用Pohozaev恒等式与Br\'{e}zis-Lieb引理, 我们证明该方程基态解的存在性.

关键词: 薛定谔-泊松-斯莱特方程, 波霍扎耶夫恒等式, 库仑-索伯列夫不等式

Abstract: This paper is concerned with the Schr\"odinger-Poisson-Slater (SPS) equations incorporating both Coulomb-Sobolev and Sobolev critical exponents in $\mathbb{R}^3$. These double critical exponents, specifically 3 and 6, lead to the non-compactness of embeddings in the relevant function space. By utilizing the Pohozaev identity and the Br\'{e}zis-Lieb lemma, we show the existence of ground state solutions.

Key words: Schr?dinger-Poisson-Slater equation, Pohozaev identity, Coulomb-Sobolev inequality

邵玉米, 雷春雨. 双临界指数的薛定谔-泊松-斯莱特方程的基态解[J]. 数学理论与应用, 2026, 46(1): 72-.

Shao Yumi, Lei Chunyu. Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents[J]. Mathematical Theory and Applications, 2026, 46(1): 72-.

双临界指数的薛定谔-泊松-斯莱特方程的基态解

Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价